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Transactions of the American Mathematical Society

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Minimal periodic orbits for continuous maps of the interval


Authors: Lluís Alsedà, Jaume Llibre and Rafel Serra
Journal: Trans. Amer. Math. Soc. 286 (1984), 595-627
MSC: Primary 58F22; Secondary 54H20, 58F11, 58F20
DOI: https://doi.org/10.1090/S0002-9947-1984-0760976-5
MathSciNet review: 760976
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Abstract: For continuous maps of the interval into itself, Sarkovskii's Theorem gives the notion of minimal periodic orbit. We complete the characterization of the behavior of minimal periodic orbits. Also, we show for unimodal maps that the min-max essentially describes the behavior of minimal periodic orbits.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0760976-5
Keywords: Periodic point, minimal periodic orbit, simple periodic orbit, unimodal map, min-max
Article copyright: © Copyright 1984 American Mathematical Society